I know one that allows the clients to clam 100sat @max 20times a day.
But the user must deposit at least once first, otherwise, it's only available when the user has 0 balance.
The name's isn't something like "free" or "faucet" (not gonna say the name).

But I agree, there's a difference.
^ That's a "casino with faucet" because here's the catch: There's an ambiguous rule "do not abuse the faucet" that sounds like "do not claim too often" (affiliate program doesn't count to that abuse since faucet claims won't even count).
On the other hand freebitco.in still functions as a faucet if you ignore the other tabs, newly created accounts can go straight to free roll.